Question: Solve for $x$ and $y$ using elimination. ${-2x-3y = -44}$ ${2x+5y = 64}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $2y = 20$ $\dfrac{2y}{{2}} = \dfrac{20}{{2}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-2x-3y = -44}\thinspace$ to find $x$ ${-2x - 3}{(10)}{= -44}$ $-2x-30 = -44$ $-2x-30{+30} = -44{+30}$ $-2x = -14$ $\dfrac{-2x}{{-2}} = \dfrac{-14}{{-2}}$ ${x = 7}$ You can also plug ${y = 10}$ into $\thinspace {2x+5y = 64}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(10)}{= 64}$ ${x = 7}$